Question

A surveyor made two sightings to the top of a mountain North of Santa Fe as shown in the picture to the right. Find the height of the mountain to the nearest foot.

Answer 1

see the attached figure to better understand the problem

in the triangle ABD
tan 29=BD/(525+x)------> BD=(525+x)*tan 29------> equation 1

in the triangle CBD
tan 38=BD/x-------> BD=x*tan 38-----------> equation 2

equals 1 and 2

(525+x)*tan 29=x*tan 38----> 525*tan29+x*tan29=x*tan38
x*[tan38-tan29]=525*tan29---> x=525*tan29/[tan38-tan29]---> x=1282.12 ft

BD=x*tan 38-----> 1282.12*tan38-----> BD=1001.71 ft-----> 1002 ft

the answer is
1002 ft